DG discretization of optimized Schwarz methods for Maxwell's equations

El Bouajaji, Mohamed and Dolean, Victorita and Gander, Martin J. and Lanteri, Stéphane and Perrussel, Ronan; Erhel, Jocelyne and Gander, Martin J. and Halpern, Laurence and Pichot, Géraldine and Sassi, Taoufik and Widlund, Olof, eds. (2014) DG discretization of optimized Schwarz methods for Maxwell's equations. In: Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, 98 . Springer-Verlag, FRA, pp. 217-225. ISBN 9783319057897 (https://doi.org/10.1007/978-3-319-05789-7_18)

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Abstract

We study here optimized Schwarz domain decomposition methods for solving the time-harmonic Maxwell equations discretized by a discontinuous Galerkin (DG) method. Due to the particularity of the latter, a discretization of a more sophisticated Schwarz method is not straightforward. A strategy of discretization is shown in the framework of a DG weak formulation, and the equivalence between multi-domain and single-domain solutions is proved. The proposed discrete framework is then illustrated by some numerical results through the simulation of two-dimensional propagation problems.

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